Internal waves and synchronized precession in a cold vapor.

Exchange in a Boltzmann gas of bosons with several internal states leads to collective transport of internal polarization. The internal dynamics can be understood as Larmor precession in the presence of a torque induced by atoms on each other via exchange coupling. A generalized Bloch equation that includes interatomic exchange effects as well as orbital motion in the gas is derived and used to interpret a recent experiment by Lewandowski et al. as an excitation of a collective wave of internal state polarization. It is shown that exchange leads to formation of domains in which precession frequencies are synchronized.